Correlation between Rushing and Time Remaining on a Task?

I realize that this might not be an easy question to answer, but I am curious if anyone else has thought about the relationship between time remaining on a task and obtaining a "successful" result from rushing.

Programing-wise, it makes the most sense to me that the probability of an incident rate (e.g., 30%) would be factored into the amount of time remaining somehow (so rushing a task that has 10 seconds left on it should be less likely to fail than rushing a task that has 10 minutes remaining). For example, it might be that each second has a 30% chance of failure, and the game does X tests to see if it fails (where X might be the number of seconds remaining). This would mean that more seconds remaining would lead to more tests, which would mean that more time remaining would be associated with more failures. This is kind of implied by the "fast-forwarding" animation in the game.

However, it also might be the case that when you click "rush", it simply determines the success/fail of the rush based upon the success rate percentage in terms of one evaluation at that percent - so it doesn't matter how much time is remaining when you rush. If you rush at 10 seconds or 10 minutes, in both cases it is simply the 30/100 chance of failing.

As mentioned below, there are factors we know affect success: SPECIAL levels, especially Luck, and previous attempts at rushing (with both successes and failures increasing the likelihood of failure).

So, my underlying question is: does amount of time remaining on a task affect the probability of successfully rushing?